---
title: "content"
description: "In HOE Beer calls the metasystem at the end of chapter 10 “schizoid — torn between present and future preoccupations” (HOE 1979: 252). System Three handles…"
url: "https://wiki.cybernetic-futures.org/pure-vsm/part-02-the-viable-system-model/ch11-system-five/ch11-system-five-content"
modified: "2026-11-12T15:26:26.024Z"
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site: "Cybernetic Futures"
---

# content

## 11.1 The Three–Four homeostat
In HOE Beer calls the metasystem at the end of chapter 10 "schizoid — torn between present and future preoccupations" (HOE 1979: 252). System Three handles the inside-and-now, System Four the outside-and-then, and neither is senior to the other. They must absorb each other's variety, and this is hard: "they do not share the same managerial nor technological languages, and their criteria of success necessarily consider different spans of time" (HOE 1979: 143).
Beer states the requirement as an axiom. The Second Axiom of Management demands equal variety between the two (HOE 1979: 298; DTS 1985: 118). In DTS it reads: "The variety disposed by System Three resulting from the operation of the First Axiom equals the variety disposed by System Four" (DTS 1985: 118). The First Axiom (see chapter 9) balanced System One against the six vertical channels; the Second balances System Three against System Four. DTS translates it into management terms: the investment "of (yes) **money**, (but also of) **time, care, talent, attention, reward** must be properly balanced, homeostatically" (DTS 1985: 118). Imbalance in either direction is dangerous: "Too much of this investment in Four, and the *inside-and-now* of the enterprise may collapse beneath your feet. Too much of this investment in Three, and you may be making the world's best buggy-whips, in which (notoriously) there is no future" (ibid.).
Hence the word homeostat. "The Three-Four homeostat is the organ of ADAPTATION for the enterprise" (DTS 1985: 120). As with all homeostats in the model, the principles of organization apply to it: "The Three-Four Homeostat \[...\] MUST OBEY THE FOUR PRINCIPLES OF ORGANIZATION" (DTS 1985: 117). Among the practical rules DTS lists for it is a dynamic one: "The *rate* at which they operate to restore equilibrium must match the mean rate of perturbation" (DTS 1985: 120).
In HOE the same dynamic requirement leads Beer to the Fourth Principle of Organization. A steady familiarity with what is going on in System Three and System Four seems to be essential, and he formulates: "The operation of the first three principles must be cyclically maintained through time, and without hiatus or lags" (HOE 1979: 258). Orthodox practice, by contrast, relies "almost wholly, on 'snapshot' accounts of the situation" (ibid.). His means is to extend the operations room of chapter 10: "Let it become the Three-Four clubhouse, and not merely a development-oriented place" (HOE 1979: 258). The resulting management centre "would replace the Boardroom, the Executive Suite, and all of those committee rooms. Here System Three and System Four would exhibit themselves to each other, in a continuous mode, and absorb each other's variety" (ibid.).
Without such machinery Beer expects a power struggle where there should be a balance: "It will be a matter of Three *versus* Four and Four *versus* Three — and one of them will WIN, as a matter of power. It usually happens. It is a signpost to disaster" (HOE 1979: 258). In practice, the requisite variety between Three and Four is achieved "by a massive variety attenuation between the two subsystems — so that for each of them the rich reality of the relative investment problem is attenuated to the rule: 'it's *them* against *us*'" (HOE 1979: 259).
## 11.2 Closure
A well-designed Three–Four homeostat still leaves a gap. Beer asks what happens if the Three–Four loops "(in their turn) result in uncontrolled oscillation? System Two cannot reach into the metasystem: it is dedicated to damping oscillations in System One" (HOE 1979: 259). The answer follows directly: "There has to be a System Five. That will do it. System Five will monitor the operation of the balancing operation between Three and Four" (ibid.).
System Five arises from the concept of closure, "whereby the viable system 'turns in on itself' to become an identity" (HOE 1979: 144). Beer introduces closure as a mathematical notion and describes it in a run of images: "Closure is the snake that is eating its own tail. Closure is what makes the language complete, self-sufficient. \[...\] Closure turns the system back into itself, to satisfy the criteria of viability at its own level of recursion. Closure is the talisman of *identity*" (HOE 1979: 260). In a parenthesis he refers to Leibniz's monadology and rejects the division of systems into "open" and "closed" used in General Systems Theory, because he cannot identify any system that is either completely open or totally closed (HOE 1979: 260). He specifies: "by 'closure' I mean a *self-referential process*, and not the isolation of the system within an adiabatic shell" (HOE 1979: 260).
DTS puts it this way: "Logical closure means above all • self-reference: the assertion of **identity**" (DTS 1985: 130). Closure also means "there is **no more**", and DTS draws the same line as HOE between logical and physical closure: "There could not be a 'System Six' — because the five-fold system is a *closed* system, in logic. (It is obviously *open* to both energy and information.)" (DTS 1985: 130). HOE gives the recursive version: "What is beyond System Five is the next level of recursion, of which *this* fivefold viable system is an operational element" (HOE 1979: 259). DTS makes the link to chapter 10 explicit: the self-reference of System Four's model of itself is "the operational basis for the final self-referencing, system-closing, System Five" (DTS 1985: 115).
## 11.3 The role of System Five
Closure has a familiar face, "the boss". However "the boss" is conceived, "this boss *supplies the closure*" (HOE 1979: 261). The autocrat does it by decree: "'that's enough; I have heard all the arguments; THIS is how it will be'. Then high variety generated between Systems Three and Four, and not absorbed between them, is CLOSED by System Five" (ibid.). Beer judges this version on cybernetic grounds as well as ethical ones: it is "extremely vulnerable, unless the boss (Five) is God Himself. Sooner or later, Five will make a destabilizing mistake" (HOE 1979: 261). The reason is variety. The autocrat can administer closure only on a heavily attenuated input, because he cannot absorb the combined variety of Three and Four.
The alternative Beer prefers leaves variety absorption to Three and Four themselves. In a working Three–Four homeostat, "All that remains for System Five is to monitor the regulatory machinery — to ensure that it does not embark on an uncontrolled oscillation" (HOE 1979: 262). This boss still supplies closure, but "He is not applying it by massive variety inhibition: he is leaving variety absorption where it belongs, between Three and Four" (ibid.). His intervention on the command axis therefore has low variety. He listens to the routine signals that all is well, and "It is only the interruption of those messages by a cry denoting imbalance and incipient oscillation that will lead to intervention" (ibid.).
Beer sums up: "cybernetically, its key role turns out to be as monitor of the variety sponge between Systems Three and Four: the administrator, as it were, of Ashby's Law in the metasystem" (HOE 1979: 144); "Within any one viable system, System Five is the metasystemic administrator of Ashby's Law" (HOE 1979: 263). The next sentence gives the variety formulation: "It necessarily absorbs the residual variety of the Three-Four interaction" (ibid.).
DTS gives the two functions in one sentence: System Five is "to supply logical closure to the viable system; and \[...\] to monitor \[...\] the Three-Four Homeostat" (DTS 1985: 129). The Third Axiom follows: "The variety disposed by System Five equals the residual variety generated by the operation of the Second Axiom" (DTS 1985: 130; HOE 1979: 567; where HOE first states the axiom, it reads "is equivalent to", HOE 1979: 298). Beer warns against assuming that the residue is small: "We often think of what is 'left over', residual, as being very small. There is nothing to stop it from being very large indeed. System Five may be absorbing more variety than anyone has realized" (DTS 1985: 130).
DTS also says how System Five sets rules. Discussing how System Four can acquire criteria of relevance for scanning the future, Beer writes: "I think that the rules come from System Five: not so much by stating them firmly, as by creating a corporate ethos — an atmosphere" (DTS 1985: 124). Published formal "objectives", he adds from experience, are "not recommended" (ibid.).
## 11.4 Who is System Five?
The boss of the organization chart is not the whole answer. The Inside-and-Now depends on Systems Three-Two-One, the Outside-and-Then on Systems Three-Four-Five, and "System THREE is the common element: it is the managerial fulcrum of viable organization" (HOE 1979: 263). Hence: "With great respect to System Five (for there sits 'the boss'), System Three in practice really runs the enterprise" (HOE 1979: 263). DTS says the same more drily: the fulcrum at System Three, "which, for this reason, usually thinks it is running the whole enterprise" (DTS 1985: 129).
Who, then, makes up System Five? "Under more democratic conventions, System Five consists of many people" (HOE 1979: 263); "except for genuine autocracies" it "includes many people — which is contrary to popular belief" (HOE 1979: 264). Beer lists possible members: heads of System One and of System Three, shareholders, a consumers' council in a nationalized industry, perhaps, in the future, trade unionists "or better still, simply workers" (HOE 1979: 263–264). He also notes a limit on its power: "Probably System Five's main problem is its belief that it is *not* the puppet of some other system, whether subsystem or metasystem. But it always is" (HOE 1979: 264). In the neurophysiological version, "The cortex has no direct connexion with either the external or the internal environment: all its input is mediated by Systems Three and Four" (ibid.).
In BOTF System Five is "the thinking part of the whole organization", which "for the body, is the cortex itself — and for the firm it is the senior management" (BOTF 1981: 201). Beer then revises the orthodox picture of top management as a tidy set of nodes. System Five is modeled as the "multinode": "System Five is not the collection of nodes, logically organized to be precise and well mannered, that our first model suggested. It is instead, whether made of neurons or managers, an elaborately interactive assemblage of elements. I call it 'the multinode'" (BOTF 1981: 205).
Chile gave Beer the political version. Explaining the model to Allende, Beer drew System Five, and before he could say that this was the President, Allende answered "*el pueblo*" (BOTF 1981: 258; HOE 1979: 264). Whatever Allende's pride in his office, Beer comments, "when it came down to cybernetic science, he — System Five — was 'the people'" (BOTF 1981: 258). HOE retells the scene and closes it with a formula that gathers up the argument of 11.2 and 11.3: "As I said, the understanding of System Five is difficult, and its nature is mysterious. Its *role* is not mysterious at all. That role is closure" (HOE 1979: 264). The first of Beer's five principles for the Chilean project reads: "System Five within a people's government cannot be an élite ruling class: it is somehow the embodiment of the mass of the people themselves" (BOTF 1981: 288).
## 11.5 The multinode and the monitoring of decisions in BOTF
Chapter Fourteen of BOTF, "The multinode—system five" (BOTF 1981: 201–223), starts from the organization chart of a top team: a chief executive MM, three directors, each with three subordinates, thirteen people in all (Figure 39; BOTF 1981: 201). Beer lets them follow the chart's protocol. Each manager consults his subordinates separately and says "yes" only if all of them do. With advisers right seven, eight and nine times out of ten, "the boss will make less than two correct decisions out of every hundred" (BOTF 1981: 203). Neurons are far less reliable than managers, yet the brain works, because neurons "reinforce each other" (BOTF 1981: 205). Figure 40, "How organizations really work", connects the same thirteen people with repeated and crossing channels, and Beer notes that, save for the letters, it could illustrate the cortex (BOTF 1981: 204–205). Recalculated on the same assumptions, the chance that the group gives the wrong answer falls to 0.0033: "It is the way to get reliable results out of unreliable components" (BOTF 1981: 207). Beer draws three admissions from this: the boss is a colleague, "*primus inter pares*", of a group that includes his subordinates; protocol "must not forbid rich interactions throughout a group"; and there is far more communication at the same level than between seniors and juniors (ibid.).
The multinode works, but "it takes far too long to work successfully" (BOTF 1981: 208). Rigorous protocol is excluded as a remedy, because "it denatures the system itself" (ibid.). The remedy Beer offers is a way of monitoring the decision in terms of information. A decision has the form "do *this*" (rather than anything else), and the aim is to "measure the variety of the complex decision at the start, measure the reduction of variety brought about by each conclusion reached in the process of thinking things out, and in general monitor the entire operation of the multinode as the variety comes down to a value of one — the decision itself" (BOTF 1981: 209). Two tools are needed. The first is a search paradigm that is "priority-free", so as not to tell the multinode in what order to decide (ibid.): the problem is described in *n* logical dimensions, as a map is searched by coordinates rather than by numbering every square (BOTF 1981: 209–211). The second is a metric, variety measured in bits (logarithms to base two), which Beer relates to entropy (BOTF 1981: 211–213).
A fabricated example follows. A new product decision has six dimensions (production, marketing, finance, staffing, research and development, distribution) with a total variety of 131,072 alternatives, or 17 bits (BOTF 1981: 215). A "decision algebra" records which variables bear on which (BOTF 1981: 216–219). When one selling plan is dropped, the ostensible reduction is 0.2 bits; followed through the dependences, "we have in fact reduced uncertainty in a single stroke by 5.84 bits" (BOTF 1981: 222). "This is the power of the multinode and its multidimensional search paradigm. It is a power which the multinode itself already has, but of which it is not quite self-conscious. That is why it needs a monitoring technique" (ibid.). The technique also shows when uncertainty rises again, because a decision has been unmade or the problem has changed (Figure 41; BOTF 1981: 222–223). One chart Beer kept had six peaks, the last as high as the first, which "can mean only that the multinode as constituted is unable to rise to the complexity of the problem it faces" (BOTF 1981: 223).
## 11.6 The higher management
BOTF closes Part Three with Chapter Fifteen, "The higher management" (BOTF 1981: 225–239). It asks why the hierarchy stops at System Five when logic points to an infinite regress of metasystems. Beer's answer is ecological, not logical: the ultimate criterion of viability is "the capability to survive. This is both a physiological and ecological criterion — and certainly not a logical one" (BOTF 1981: 226). Setting the cut-off at viability "solves the problem of identity, although it does not solve the problem of the undecidable" (ibid.). Elaborating the model yields subsystems and "trans-systems", not "a new metasystem, a System Six" (ibid.). Beer notes the relation to the later book himself: the criteria in BOTF are "neurocybernetic criteria; a set of logical criteria is developed in the companion volume, *The Heart of Enterprise*" (ibid.; compare the logical closure of 11.2).
What remains is "one trick": to stand outside ourselves and survey what we are, a faculty Beer calls "*the higher management*" (BOTF 1981: 227). The term does not refer to seniority, and it is not "meta-management", "because we are bound to include everything we know and understand about the control of the viable system in System Five. This is not then a metasystemic activity, but almost *extra*systemic" (ibid.). Its subject is identity, which Beer finds reasserted in participation, accountable cost and profit centres, decentralization and corporate planning (ibid.). The chapter then states the Recursive System Theorem (BOTF 1981: 228; see chapter 6).
The last part of the chapter returns to the algedonic mechanism modelled on the reticular formation, now as a variety reducer. With redundancy of potential command, a notion Beer takes from McCulloch, any group that holds the relevant information may become the centre of decision (BOTF 1981: 232). "Thus it comes about that the algedonic controller, for both the brain and the firm, is the biggest variety reducer of them all. It determines the *mode* of behaviour" (BOTF 1981: 233). For firms Beer describes mutually exclusive modes: sustained activity, growth and retrenchment on one scale, then crisis, the moribund, self-destruction, and "unfeigned aggression", which he calls "The sixth mode" (BOTF 1981: 234–235). He then speaks of "these six" (BOTF 1981: 236), although seven are named. The controller "is indeed a trans-system. Essentially, it connects System Three with System Four, but in so doing it creates a new dimension of decision, geared to survival" (BOTF 1981: 237). Once the mode is fixed across Three and Four, "System Five can act (albeit in a most superior capacity) only within the context of this conclusion" (BOTF 1981: 238). Beer italicizes the consequence: "*The senior controllers inevitably work within the framework set by their juniors*" (ibid.).

## References

- **HOE** — Beer, Stafford (1979). *The Heart of Enterprise*. Chichester: John Wiley & Sons.
- **BOTF** — Beer, Stafford (1981). *Brain of the Firm*. 2nd ed. Chichester: John Wiley & Sons. (1st ed. London: Allen Lane, 1972.)
- **DTS** — Beer, Stafford (1985). *Diagnosing the System for Organizations*. Chichester: John Wiley & Sons.